Article

# Magnetic dipole moments of the spin-$$\frac{3}{2}$$32 doubly heavy baryons

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## Abstract

The magnetic dipole moments of the spin-$$\frac{3}{2}$$ doubly charmed, bottom and charmed-bottom baryons are obtained by means of the light-cone QCD sum rule. The magnetic dipole moments of these baryons encode essential knowledge of their inner structure and shape deformations. The numerical results are given by $$\mu _{\Xi _{cc}^{*++}} = 2.94 \pm 0.95$$, $$\mu _{\Xi _{cc}^{*+}} = - 0.67 \pm 0.11$$, $$\mu _{\Omega _{cc}^{*+}} =- 0.52 \pm 0.07$$, $$\mu _{\Xi _{bb}^{*0}} = 2.30 \pm 0.55$$, $$\mu _{\Xi _{bb}^{*-}} = -1.39 \pm 0.32$$, $$\mu _{\Omega _{bb}^{*-}} = -1.56 \pm 0.33$$, $$\mu _{\Xi _{bc}^{*+}} = 2.63 \pm 0.82$$, $$\mu _{\Xi _{bc}^{*0}} = - 0.96 \pm 0.32$$ and $$\mu _{\Omega _{bc}^{*+}} =- 1.11 \pm 0.33$$, respectively.

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... The numerical results are given in Tables II-XV. In addition, we compare our results with experimental values and other theoretical models, including HBχPT [63,64,[80][81][82][83], the HCQM [56][57][58][59]84], QCDSR [60], CI [61], LQCD [62,72,85], the pion meanfield approach [66], heavy quark symmetry (HQS) [54], the chiral quark model (χQM) [86,87], the chiral constituent quark model (χCQM) [88], the bag model (BM) [76], the NRQM [89], the relativistic three-quark model (RTQM) [90], covariant baryon chiral perturbation theory (BχPT) [91][92][93], the light cone QCD sum rule (LCQSR) [94][95][96][97][98][99][100][101][102][103], the hypercentral model (HCM) [104][105][106], the covariant spectator quark model (CSQM) [107], χPT [108], the chiral quark soliton model (χQSM) [109,110], and the constituent quark model (CQM) [111]. ...
... In contrast to the EMS, our results in SQCS are more compatible with other models [76,81,88,89,105,106]. As shown in Table XI [89], and the HCM [105], except for the LCQSR [99], which predicts larger numerical values among other theoretical models. The numerical predictions for the magnetic moment of Ξ Ãþ cc , however, differ between models. ...
... (iv) The magnetic moments of Ξ Ãþ cc and Ω Ãþ cc are expected to be small, as the contributions of the heavy quarks and the light quark cancel out to some extent due to their opposite signs. However, in the LCQSR [99], the contribution from the light quark dominates over two charm quarks, with a large magnitude leading to larger numerical values. ...
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... iii. Similarly, for the doubly charmed baryons, our results compare well with the predictions of χCQM [81], NRQM [83], and HCM [93], except for LCQSR [98] which predicts larger numerical values among other theoretical models. The numerical predictions for the magnetic moment of Ξ * + cc , however, differ between models. ...
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... MeV is the nucleon mass. For the convenience of comparison with the magnetic moments of the doubly charmed baryons μ T obtained in other approaches [21][22][23][24][25][26][27][28][29]48], we take the nuclear magneton μ N as the units of μ T in this work. ...
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... Specifying the magnetic moment provides important information on structure, size, and shape of hadrons as well as hadron properties based on quark-gluon degrees of freedom. Magnetic moments of the doubly-heavy baryons have been examined broadly in the literature, see [62,[90][91][92][93][94] for recent references. ...
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We review the description of the lowest-energy nucleon excitation—the Δ(1232)Δ(1232)-resonance. Much of the recent experimental effort has been focused on the precision measurements of the nucleon-to-ΔΔ transition by means of electromagnetic probes. We confront the results of these measurements with the state-of-the-art calculations based on chiral effective-field theories (EFT), lattice Quantum Chromodynamics (QCD), large-NcNc relations, perturbative QCD, and QCD-inspired models. We also discuss the link of the nucleon-to-ΔΔ form factors to generalized parton distributions (GPDs). Some of the theoretical approaches are reviewed in detail, in particular, recent dynamical and unitary-isobar models of pion electroproduction, which are extensively used in the interpretation of experiments. A novel extension of chiral EFTs to the energy domain of the ΔΔ-resonance is reviewed. The two-photon exchange effects in the electroexcitation of the ΔΔ-resonance are addressed.
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The spectra of baryons which include two heavy quarks can be treated as a two-body system, where the two heavy quarks constitute a bosonic diquark. We derive the effective potential between the light quark and the heavy diquark in terms of the Bethe-Salpeter equation. To obtain the spectra, several serious problems need to be solved: (1) the operator ordering, (2) the errors caused by the nonrelativistic expansion, (3) spin-spin coupling, and (4) the mixing between the scalar-diquark-baryon and vector-diquark-baryon. In this work we take reasonable approaches to deal with them.
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We compute the electromagnetic properties of \Xi_cc baryons in 2+1 flavor Lattice QCD. By measuring the electric charge and magnetic form factors of \Xi_cc baryons, we extract the magnetic moments, charge and magnetic radii as well as the \Xi_cc \Xi_cc \rho coupling constant, which provide important information to understand the size, shape and couplings of the doubly charmed baryons. We find that the two heavy charm quarks drive the charge radii and the magnetic moment of \Xi_cc to smaller values as compared to those of, e.g., the proton.
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Spectra of masses are calculated for the families of doubly heavy baryons in the framework of the nonrelativistic quark model with the QCD potential of Buchmüller and Tye. We suppose the quark-diquark structure for the wave functions and take into account the spin-dependent splittings. The physical reasons causing the existence of quasistable excited states in the subsystem of heavy diquark are considered for the heavy quarks of identical flavors.
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We compute the magnetic moments of charmed baryons using the gauge-theory quark model of De Rújula, Georgi, and Glashow. We find that these moments are quite different (sometimes differing in sign as well as magnitude) from those computed by Choudhury and Joshi, who used U(8) symmetry. The reason for the difference is that in our calculation the heavy mass of the charmed quark badly breaks U(8) symmetry. Our results reduce essentially to those of Choudhury and Joshi when all quark masses are set equal to one another.
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The mass spectrum of charmed and bottom baryons is computed on anisotropic lattices using quenched lattice nonrelativistic QCD. The masses are extracted by using mass splittings which are more accurate than masses obtained directly by using the nonrelativistic mass-energy relation. Of particular interest are the mass splittings between spin-1/2 and spin-3/2 heavy baryons, and we find that these color hyperfine effects are not suppressed in the baryon sector although they are known to be suppressed in the meson sector. The results are compared with those obtained in a previous nonrelativistic QCD calculation and with those obtained from a Dirac-Wilson action of the D234 type.
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We investigate the charmed baryon mass spectrum using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3 \times 64$ lattice. The dynamical up-down and strange quark masses are tuned to their physical values, reweighted from those employed in the configuration generation. At the physical point, the inverse lattice spacing determined from the $\Omega$ baryon mass gives $a^{-1}=2.194(10)$ GeV, and thus the spatial extent becomes $L = 32 a = 2.88(1)$ fm. Our results for the charmed baryon masses are consistent with experimental values, except for the mass of $\Xi_{cc}$, which has been measured by only one experimental group so far and has not been confirmed yet by others. In addition, we report values of other doubly and triply charmed baryon masses, which have never been measured experimentally.
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Using several realistic interquark potentials, the ground-state energies of all the baryons containing one, two or three heavy quarks of type c or b are studied within a non-relativistic quark model. The three-body problem is rigorously solved using the Faddeev formalism. Various static properties, such as mass radii, charge radii, magnetic moments, and wave functions at the origin are calculated as well. The complete spectrum for all these baryons is computed using a harmonic-oscillator basis with states up to 8 quanta. Emphasis is put on the levels lying below the thresholds corresponding to quark-pair creation.
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The masses of charmed baryons with spin 1/2 (Λ c +,Σ c ++) and their residues into quark currents are calculated on the basis of QCD sum rules method. The obtained values of masses are in good agreement with experiment. Arguments are given in favour of existence of resonance Σ c ++ * with negative parity and mass close to 2, 6 GeV.